Mathematics and Ray optics | test no. 2

Question no. 1

If x = cost , y = sint , then what is equal to ?
y^-3
  y³
  -y^-3
  -y³

Question no. 2

What is the derivative of (log_tanxcotx)(log_cotxtanx)^-1 at x = π/4 ?
  -1
  0
  1
  1/2

Question no. 3

What is the derivative of log₁₀(5x² + 3) with respect to x ?
(xlog₁₀e)/(5x² + 3)
  (2xlog₁₀e)/(5x² + 3)
  (10xlog₁₀e)/(5x² + 3)
  (10xlog_e10)/(5x² + 3)

Question no. 4

Let f(x) = [|x| -|x-1|]² , What is f'(x) equal to when x > 1 ?
  0
  2x-1
  4x - 2
  8x - 4

Question no. 5

let f(x+y) = f(x)f(y) for all x and y . then what is f'(5) equal to ?
  f(5)f'(0)
  f(5) - f'(0)
  f(5)f(0)
  f(5) + f'(0)

Question no. 6

y = ln(√tanx) , then what is the value of dy/dx at x = π/4 ?
  0
  -1
  1/2
  1

Question no. 7

let g(x) = x³ - 4x + 6 . If f'(x) = g'(x) and f(1) = 2 , what is f(x) equal to ?
  x³ - 4x + 3
  x³ - 4x + 6
  x³ - 4x + 1
  x³ - 4x + 5

Question no. 8

If f(x) = e^sin(logcosx) and g(x) = logcosx , then what is the derivative of f(x) with respect to g(x) ?
  f(x)cos[g(x)]
  f(x)sin[g(x)]
  g(x)cos[f(x)]
  g(x)sin[f(x)]

Question no. 9

What is the derivative of log_x5 with respect to log₅x ?
-(log₅x)^-2
  (log₅x)^-2
  -(log_x5)^-2
  (log_x5)^-2

Question no. 10

Which of-the following is not a property of light?
It can travel through vacuum
It has a finite speed
  It requires a material medium for its propagation
  It involve transportation energy

Question no. 11

When light travels from one medium to another, which of the following does not change?
  frequency
  refractive index
  velocity
  wavelength

Question no. 12

The air bubble inside water shine due to:
  Reflection
  Refraction
  T.I.R.
  None of these

Question no. 13

The angle of deviation for a prism is greatest for:
  violet
  red
  orange
  yellow

Question no. 14

A certain far-sighted person cannot see objects closer to the eye than 100 cm. The power of the lens which will enable him to read at a distance of 25 cm will be?
  3D
  1D
  4D
  2D

Question no. 15

The refractive indices (R.I.) of glass and water with respect to air are 3/2 and 4/3 respectively. The R.I. of glass w.r. to w ater is:
  8/9
  9/8
  7/6
  2